Preheat the oven to 425°F and set an oven rack in the middle position. Line a 13x18-in baking sheet with parchment paper.

In a large bowl, whisk together the flour, cornstarch, baking powder, baking soda, granulated sugar, and salt.

Add the pieces of cold butter. Use your fingertips to rub the butter into the dry ingredients until the mixture resembles coarse crumbs with pea-sized clumps of butter within. Add the buttermilk and stir with a rubber spatula until the dough comes together into a sticky, shaggy mass. Do not overmix.

With lightly floured hands, form the dough into 8 craggy-looking balls and place on the prepared baking sheet. Sprinkle the tops with the turbinado sugar. Bake for 13 to 15 minutes, until the biscuits are golden.

Put one-third of the berries in a medium bowl and, using a potato masher or a fork, mash them into a chunky purée. Mix in the remaining berries, along with the raspberry jam and granulated sugar. Let the berries sit at room temperature for about 10 minutes, until saucy.

In the bowl of an electric mixer fitted with the whisk attachment, whip the heavy cream until soft peaks form. Sprinkle the granulated sugar over the cream and beat until soft peaks return. Do not overbeat.

To assemble the shortcakes: Using a serrated knife, split the biscuits in half horizontally and transfer the bottoms to 8 dessert plates. Spoon about three-quarters of the macerated berries and their juice evenly over the biscuit bottoms. Top with a generous dollop of whipped cream and cover each with a biscuit top. Spoon more berries and cream over each shortcake and serve immediately.